A couple of related improvements to how we build the Dockerfile:

1. Don't invalidate the Python dependencies layer just because
   `package.json`, `gulpfile.js` or `scripts/` changed.
2. Use a prebuilt node-sass binary. The prebuilt binaries supplied by
   the node-sass project aren't compatible with Alpine Linux (which uses
   musl-libc rather than glibc).
3. Make some small tweaks to the gulpfile so we can build just the
   assets needed for the web application (i.e. skipping the extension).